Electronica-F3-Miguel Yapur
July 25, 2022 | Author: Anonymous | Category: N/A
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H]MXHDA ]XSH_NL_ SLDNUUÎMBNMA EHD DNUL_AD @AMXDUAE EH NBKHBNH_ÆA HB HDHMU_NMNEAE ^ MLFSXUAMNÝB
HDHMU_ÝBNMA NNN
@LDDHUL EH HJH_MNMNL] _H]XHDUL]
S_L@H]L_: NBK. FNKXHD ^ASX_ _HADNZAEL SL_: JXAB E_XHU A. ML__HKNEL SL_: K_AMH DÝSHZ M.
NN UH_FNBL ?33>
HJH_MNMNL 1
Eatls: E1, E?: 1B533; X1,, X?, X1 X?, X=: X=: DF=1 DF=1; ;
Na Naej ej68 683b 3bA A
Pi61,?P
PB_ (fnb)6=3P
PB_ (fax)6==P
Mlb S1 y S? hb plsnmnýb mhbtrad, rhadnmh ub kra`ml eh Pl vs Nl. Ehsarrlddl: Abádnsns eh da htapa eh X=:
Plu lutt 6 P`jl `jl Perlp erlplu lutt 6 Pe Pen n fnb Pnb ∟ Plut ≨ P`jl 3,8P ?P
Pen fnb6 Perlplut
Pi= 6 1,?P
Slr mlb`kuramnýb ehd Df=1; usafls da ýrfuda:
S? Pl ∟ Pi= 1 + û + NAEJ = kS? 6 3 _? Nl 6
1,8 + 3,38k1, 1, 86 10,?7P û 3,1?
Pl 6 1,?1 +
Pl 10,?7P 6 6 715 fA _= 3, 3?I
Abádnsns eh da htapa X?:
Px 6 Pl + Pe=⇟ Px( fnb) 6 Pl( fax) + Pe=( fnb) Pl( fax)
6 = 1,?Y PV ⇟ Px( fnb) 6 =1,?P + ?P 6 ==,?P
NX? 6 NAEJ ? +
Pi? 1,?P 6 3,38fA + 6 13,38fA _5 3,1?i ℠
Mlfl 3,38YfAV hs ehsprhmnaodh mlfparael mlb dls 13YfAV, hbtlbmhs bl dl usafls.
Abádnsns eh da htapa eh X1: Suhstl quh 13Y fAV 22 83Y uAV , hbtlbmhs ehsprhmnafls
. ]n X1 lphra hb da zlba dnbhad
hbtlbmhs: (plehfls usar hd hqunvadhbth ehd DF=1;). + ∟ Plut 4 Pl( X1) 4 PB_ ⇟ PXA 6 PX A
Aehfás
Pe12 Pmhsat ( Q1)
≈ ?P
P_1 + P S1A 6 Pi16 1 1,,?P N_1 k_1 + 13kS1A 6 1,?P N_1 6 13 + Nx
( 13 + Nx) k_1 + 13kS 1A 6 1,?Y PV Nx 6
S1 1,? ∟ 13kS1A ∟ 13k_1 9 S1A 6 _1 ?
1,?∟ 13( 3,3;8) ∟ 13( 3,331) Nx 6 3,331 ]n Nx 4 1118 fA ⇟ PX+A 2 PX∟A
6 1118 fA
∵Q1shs hsa aturay ayP Px 6 PB_ ∟ Pmhsat ( Q1) .
]n Nx Nx 2 1118 fA ⇟ PX+A 2 PX∟A ∵Q1aufhbta s su uPmh( Q1) ⇟ Plut ensfnbuyh gasta quh Nx 6 1118 fA .
PlYPV 10,?
NlYfAV 715
Hb buhstrl abádnsns ghfls asufnel quh dls mnrmuntls eh prlthmmný prlthmmnýb b eh M.N. X1 bl gab amtuael, hstl hs:
• Dnfntamnýb eh mlrrnhbth • Srlt Srlthmm hmmnýb nýb par para a ub ubmn mnlb lbafn afnhbt hbtl l hb hd ár árha ha eh lp lphr hramn amnýb ýb shk shkur ura a eh dls •
trabsnstlrhs nbthrbls. Dnfntamnýb tîrfnma.
• Hb rhadneae a adtls vldtajhs enhrhbmnadhs Pe, da prlthmmnýb para lphramnýb
hb hd árha shkura ensfnbuyh da dnfntamnýb eh mlrrnhbth. Mlb hd DF=1;, da fáxnfa mlrrnhbth hs plsnodh snhfprh quh Pe 4 18P y sn Pe 6 18P úbnmafhbth sh ensplbh eh da sadnea eh 533YfAV.
Hqunvadhbth ehd DF=1;
HJH_MNMNL ?
Eatls:
ºM [
Naej 6 3, Se ( fax) 6 ?3Y [V aUa 6 58º M9 η jm 6 ?,= DF=1;: Uj ( fax)
6 183ºM9
ºM 9 Pi 6 1,? P Y V [
η ja 6 = 8
Enlels: Pe 6 3,;P
Zhbhr: _e ≈ 3 (rhsnsthbmna enbáfnma) Srhkubtas:
1. Madmu Madmudh dh hd rab rabkl kl e eh h _? p para ara q quh uh 3 ≥ Pd ≥ ?8P ?. ]n par ara a Nd 6 833Y fAV , P B_( fnb)
m admudh hd vadlr eh . 6 ?7P, madmudh =. Madmu Madmudh dh hd vad vadlr lr eh M? p para ara q quh uh N z fnb 6 ?Y fAV . 5. ]n Pd 6 1?P y 3Y fAV ≥ ND ≥ 833Y fAV . Madmudh da plthbmna ensnpaea plr hd DF=1; y hd ensnpaelr sn hs bhmhsarnl Ua6 58ºM.
Ehsarrlddl: Htapa eh fabhjl eh Slthbmna. Mlbsnehramnlbhs: : slb mnrmuntls aonhrtls hb hstael hstaodh. Sldarnzael nbvhrsafhbth (bl mlbeumh).
_hkud _hkuda a hd vldtaj vldtajh. h. Hs ub zhbhr zhbhr eh rh rhhr hrhbm hbmna na nbthkr nbthkrael ael hb ub sldl sldl mgnp mgnp ml mlb b mnrmunth mnr munthræa ræa eh mlfphbsam mlfphbsamnýb nýb eh thfphratura thfphratura h nfpheabmna nfpheabmna enbáfnma enbáfnma eh 3,0 lgfnls. ]u mlh` mlh`mn mnhbt hbth h eh th thfp fphra hratu tura ra hs eh 3,331%[ ºM da tldhra tldhrabmn bmna a ehd 8% hstaon hstaondne dneae ae ehd 3,33?% y mlrrnhbths eh lphramnýb hbtrh hd 3,0 YfAV y 18 YfAV.
Mádmudl eh rabkl eh _?: Asufafls quh dls trabsnstlrhs nbthrbls QxyQy ehd DF=1; lphrab hb zlba dnbhad hstl hs:
Pmh 6 Pbr ∟ Pd 2 Pmhsat ( Qy)
6 ?P
x 4 Pbr ( fnb) ∵ P+( XW ) ]n hd lp-afp Xx lphra hb zlba dnbhad ⇟ Pd 4 P
6 3.
Hbtlbmhs: P d ∟ Pa 6 1,?P 6 Pi
Po o + NNrr1( _1 + _? + _=) Aehfás: Pd 6 P Pd 6 Pz + Pn ∟ Pak( _1+ _? + _=) _1 Pd 6 ∟0,>P +
1,?P k( 3,1? + _? + 3,80) 3,1?i ℠
Pd 6 ∟3,1+ 13* _? ]n 3P ≥ Pd ≥ ?8P 3P 6 3,1 + 13_?( f fnnb) ⇟ _?( fnb) 6 13℠ ?8P 6 3,1+ 13_?( f fa ax) ⇟ _?( f fa ax) 6 ?8i℠ Mádmudl eh vadlr eh
PB_( p ∟ p) PB_ PB _( EM)
%6
:
PB_( p ∟ p) 1 PB_( fnb) + û PB_( p ∟ p) ?
%
PB_( p∟ p)
=?,5P ∟ ?7P %6 6 15,0% 1 PB_ PB _( EM) ?7P + û 5P ?
Da marka hb da htapa bl rhkudaea hs phsaea, fáxnfl 13% para marka dnkhra. Eh das murvas eh marka hxphrnfhbtadhs para rhmtn`mamnýb eh lbea mlfpdhta tnpl puhbth y mlb vldtajhs shmubearnls eh ?5YvV sh tnhbh:
Nr1 6
Pd ∟ Pa Pi 1,? 6 6 6 13 fAMtth _1 _1 3,1?
Nz 6 Nr5 ∟ Nr1⇟ Nr5 6 Nz + Nr1 Mlfl Nz( fnb) ⇟ Nr5( fnb) ∵Nr5( fnb) 6 ? + 13 6 1? fA ↟ Slr Slr taoda hd vadlr eh M1 6 1333 u@ . Mádmudl eh M?.
Ppi 6 Ps? ∟ ?Pe ⇟ Ppi 6 ?( 1?.0)
∟ ?( 3.;) ⇟ Ppi 6 10.5P
P_5 6 1?Y fAV ( 533℠ ) ⇟ P_5 6 5.7Y PV PB_fnb 6 Pz + P_5 ⇟ PB_ FNB 6 5.7 + 0.>⇟ PB_FNB 6 11.;P PB_EM 6
PB_ FA FAW + P B_FN FNB B ?
10.5 ∟ 11.; ⇟ PB_EM 6 ⇟ PB_EM 6 15.38P
?
PB_SS 6 PB_FAW ∟ PB_FNB ⇟ PB_SS 6 10.5 ∟ 11.;⇟ PB_SS PB_SS
6 5.;P
≥ / 13%PB_EM ⇟ Marka Shsaea Slr taoda M? 6 ??3 u@
Slthbmna Ensnpaea
SEns 6 ( Pnb ∟ Plut ) S_LF kNLXU ⇟ SEN] 6 ( PB_FAW ∟ Pd ) k833 fA SEN] 6 ( =5.? ∟ 1?) k3.8⇟ SEN]FAW 6 11.1 [ Uj 6 U A + SE ( η JA ) ⇟ Uj 6 58 º M + 11.1Y [V k =8ºM û ⇟ Uj 6 5==º M [ Bhmhsnta ensnpaelr ya quh: UjFA FAW W 6 183º M ≥ Uj 6 5==º M
UjFAW 6 UA + SE ( η JM + ηMA + ηEA ) ⇟ 183º M 6 58º M + 11.1Y [V ( η J M + ηEA )
η JM
+ η EA 6
1 83º M + 58º M 11.1Y [ V
ηEA 6 1;.80
ºM ∟ η JM ⇟ ηEA 6 1;.80 ∟ ?.=⇟ ηEA 6 1 8 .?0 [ [
ºM
HJH_MNMNL =
Eatls:
Q1: Ness 6 13 fA, Pks 6 ?P Ez: Pz 6 0,?P p pa ara Nz 6 ?3 fA, Sz 6 3,8Y [V a Ua 6 ?8º M, _e 6 1?℠ X?: maramthræstnmas prámtnmafhbth nehadhs
E1,E?,E=,E5: Pe 6 3,;P
U1: nehad
X1 rhkudaelr eh vldtajh `jl eh 8 P, Pen
6 ?P NNq q 6 0 fA
Srhkubtas:
1. _had hadnmh nmh dls maf mafon onls ls qu quh h Xe. mlbs mlbsneh nehrh rh bhmh bhmhsar sarnl nls s pa para ra quh hd hsq hsquh uhfa fa pdabthael ubmnlbh mlfl ub rhkudaelr eh vldtajh `jl ?. Madmu Madmudh dh ml mlb b fak fakbntu bntuehs ehs da das s vldt vldtajhs: ajhs:Py,Pz Ehsarrlddl:
Asufafls das snkunhbths mlbenmnlbhs eh lphramnýb para hd rhkudaelr eh vldtajh `jl: ]n Pen
2 ?P ⇟ Pi 6 8P
P+ 6 P∟ 6 Pz
⇟ Hd lp-afp X? lphra hb zlba dnbhad. ]n 3 4 Pk 4 Pd ⇟ P+
yPz z Mádmudl eh : Pd yP
6 P∟
Nz 6
Pd ∟ P Pz z 1,0Pz ∟ Pz 6 6 1,17Pz _5 3,81
Pz 6 0,38P9 Nz 6 ;,1=fA
Hd Jht Q1 lphra hb da rhknýb amtnva sn:
Pks Pse 2 Pse( sat ) ⇟ Ns Nse e 6 Ns Nse e( sat ) 1∟ û Pp
?
Duhkl Pd 6 1,0 kPz 6 1,0 ( 0, 38P )
Blth quh asufnfls quh _e 6 3
Aehfás Pse 6 Pp ∟ Pks
Mlfl P+
Hd zhbhr Ez amtúa amtúa hb da zlba eh rhkudamnýb eh vldtajh
Pd 6 P Pz z + Pz
6 P ∟ _? _? 6 Pz 1+ û _= _=
]n Nz 2 3 ↟ Pz 6 Nz + 5>0,8
Pd 6 0,?P 1 + 0i ℠ û 13i ℠
_hdamnýb Nz ∟ Pz para para hd zhbhr Ez
Pd 6 Pi + Pse ↟ Pse 6 Pd ∟ Pi
7=,=
f6
6 >,07P
6 >,>?P
Pse 6 >,07P ∟ 8P 6 5,07P
∀Nz ?3fA ∟ 3 1 6 6 _e e ∀Pz 0,?P ∟ Pzi _
Aehfás: Nse 6 NQ 6 0 fA
fA P
_e 6 3,31?Y i℠ V ↟ f6 7=,=
⇟ Pzi 6 8,>0P Nz ∟ ?3 6 f6 7= 7=,,=9 Pz ∟ 0,? Nz 6 ( 7=,=kPz ∟ 5>0, 8) Y fAV ]nhfprh quh Pz 2 Pzi 6 8,>0P
?
Pks Ns Nse e 6 Ns Nse e( sa sat ) 1 ∟ û 9 Pp Nse( sat ) 6 13 fA, P Pp p 6 Psk( l ) 6 ∟?P Psk 6 ?,5 ∟ ? 6 ∟3, 58P
Pse( sat ) 6 Pp ∟ Psk 6 ? ∟ 3,58 6 1.88P Pse 6 5,70 2 Pse( sat) 6 1,88P
⇟ Q1lp lph hra rah hb zlb lba a am amtnv tnva a
HJH_MNMNL 5
Sara hd snkunhbth mnrmuntl hbmuhbtrh:
yPl? a). Xba hxprhsnýb dnthrad para dls vadlrhs eh vldtajh Pl1 yPl o). Hvaduî das hxprhsnlbhs para dls hxtrhfls eh dls plthbmnýfhtrls plthbmnýfhtrls dnbhadneae eh dls hdhfhbtls .
y
Mlbsnehrh:
Pbr 6 Y 17P9 ?3PV
Q1: P Po oh 6 3,;P9 Pmh 6 ?P
Nm1: Pl 6 1,?P9 =;P ( aej ) 9 Nl( fax) 6 1,8A9 Pnb( fax)
6 53P9 Pen ( sat ) ≥ ?P
Nm?: P Pl l 6 ∟1,?P9 ∟ =;P ( aej ) 9 Nl( fax) 6 1,8A9 Pnb( fax)
6 ∟53P9 Pen ( sat ) ≥ ?P
Ehsarrlddl: Asufl, enlels zhbhr —lb —lb‖, ‖, lp-afps, X1: O y X1: M hb zlba dnbhad.
Px 6 Pz1
_1 + S1o _1 + S1
Nh 6
Px ∟ Pz1 _H
Nm 6
P1 ∟ 3 _=
vhrn`mabel da
Nm ≇ NNh h( krabeh)
aPz1∟ Pz1 Pl1 _1+ S1o ⇟ a6 ⇟ 6 _1 + S1 _= _H
Ehsphjabel
Pl16
_= _= _1 + S1o ∟ 1û ( a ∟ 1) kPz1⇟ Pl1 6 Pz1 _H _H _1+ S1
_= S1a ⇟ Pl16 Pz1 ∟ û _H _1+ S 1 S?o Pl1 ∟ P Py y Py ∟ Pl? _8 Py 6 Pz? ⇟ 6 ⇟ ( Pl1∟ Py) 6 Py ∟ Pl?
Pl16 Pz1
_= _1+ S1o ∟ _1∟ S1 û _H _1+ S1
S?
Pl? 6 Py + Pl? 6 Pz?
_5
_8 _8 Py ∟ Pl1 _5 _5
S?o _8 + _5 S? _5 û
_8
_5
_8+ _5 _8 ∟ _5 _5
↟ Pl? 6 Py
_8 _= S1a ∟ Pz1 k ∟ û _5 _H _1 + S 1
o)
S1a 13i℠ ∟ û 6 S1a i i i ℠ ℠ + ℠ 1 3 8 1 3 S1a 13i℠ + 13i℠ 13i℠ 13i℠ S1o 13 Pl? 6 8P ∟ ( ∟18) P û û ∟ û 6 S1o ∟ S1a û û 13i℠ 8i℠+ 1 3i℠ 13i℠ 13i℠ 13i℠ Pl16 ∟18P
Dnbhadneae
Z1: N_z N_z1 6
Pz1 + Pbr 23 _z 1
Z?: N_z N_z? 6 Pbr ∟ Pz ? 2 3 _z ?
Pbr 2 ∟Pz 1
Pbr 2 Pz ?
8+ S1o Q1: Px 6 ∟18k 6 ∟8∟ S1o 18 Nh6
Px ∟ Pz1 ∟8 ∟ S1o ∟ ( ∟18) 6 _H 13
13 ∟ S1o 2 3
6
13 ∟ S1o 23 13
⇟ S1o 4 13iY ℠V snhfprh dnbhad
A1: P1 6 Pl1 ∟ Pi
A?: P? 6 Pl? ∟ Pi
Nm1: Pen 6 Pbr ∟ Pl1
Nm?: Pen 6 Pl? ∟ Pbr
Masl 1:
S1a 6 13iY ℠ V S?a 6 13iY ℠ V ↟ Pl16 13P9 Pl? 6 3 ∟ 13P ↟ Pl?6 ∟13P S1o 6 3
S?o 6 3
A1: P1 6 1 13 3P ∟ 1,?P 6 7,7P A?: P? 6 ∟13P + 1,?P 6 ∟7,7P
17 dnbhad ∟ 18P 47 4 7, 7P 4 û P Zlba dnb ? 3 ∟17 dnbhad ∟?3û P 4 ∟7, 7P 4 8P Zlba dnb
17 7 1 3 ∟ 6 û P Zlba dnbhad û ? 3 13
Nm1: Pen 6
Nm?: Pen 6 17û ?3
∟ 136 7û P Zlba dnbhad 13
Masl ?:
S1a 6 13iY ℠ V S?a 6 3 ↟ Pl1 6 13P9 Pl? 6 13P ∟ 13P ⇟ Pl? 6 3P S1o 6 3i℠
S?o 6 13i℠
A?: P? 3P 1,?P 1,?P
6
+
6
A1: P1 6 1 13 3P ∟ 1,?P 6 7,7P
∟17 P P P Zlba dnb dnbhad ∟?3 û 4 1, ? 4 8 17 dnbhad ∟ 18P 47 4 7, 7P 4 û P Zlba dnb ? 3
17 7 1 3 ∟ 6 û P Zlba dnbhad û ?3 13
Nm1: Pen 6
17 adnnbhad û P Zlbad ? 3
Nm?: Pen 6
Masl =:
S1a 6 3Y ℠ V S?a 6 13iY ℠ V ↟ Pl1 6 3P9 Pl? 6 3P ∟ 3P ↟ Pl? 6 3P S1o 6 13iY ℠V
S?o 6 3Y ℠ V
A1: P1 6 3P ∟ 1,?P 6 ∟1,?P A?: P? 6 3 + 1,? 6 1,?Y P V
17 17 P 3 ∟ 6 û P Zlba dnbhad û ? 3 ?3
Nm1: P Pe en 6
Nm?: Pen 6 1 adnnbhad P Zlbad ?7 3û
Masl 5:
S1a 6 3Y ℠ V S?a 6 3Y ℠ V ↟ Pl16 3P9 Pl? 6 13P ∟ 3P ↟ Pl?6 13P S1o 6 13 13iY ℠V
S?o 6 1 13 3iY ℠ V
A1: P1 6 3 ∟ 1,?P 6 ∟1,?P A?: P? 6 13P + 1,?P 6 11,?P
↟ A? saturael ⇟ P? 6 8P
↟ Pl? 6 P? ∟ Pi 6 8P ∟ 1,?P 6 =,7P 17 17 3 ∟ û 6 ?3 û P Zlba dnbhad ? 3
Nm1: Pen 6
HJH_MNMNL 8
Sara hd snkunhbth hjhrmnmnl khbhraelr eh shñad
a) Fuh Fuhstr strh h da hxpr hxprhsn hsnýb ýb dnthr dnthrad ad y hd va vadl dlrr bu bufîr fîrnml nml par para a hd phrn phrnle lel l eh das shñadhs khbhraeas. vadlrhs hs eh vldtajh y eh tnhfpl. o) Kra`quh Pl( t ) 6 Py( t ) , Pm( t ) flstrabel dls vadlr Ehsarrlddl:
= 6 ;,8P Px 6 13Pk =+ 1
↟
N6
13 ∟ Px 6 13 ∟ ;,86 ?,8fA 1
*]n Pm( t 6 3) 6 3P ? A1: Pm ∟ k13 6 Pm ∟ 0,0; 6 3P ∟ 0,0;P 6 ∟0,0;P = Mlfl hs (-) hbtlbmhs
Mlfl hs (+) hbtlbmhs
_
≡ G
↟ Q 6 D↟ Qa 6 l l y yP Py 6 13P
Px ∟ 3,; ∟ Py ;, 8P ∟ 3,;P ∟ 13P 6 6 ∟3,=?f 13 13i ℠ ⇟ Q? 6 Mlrth∵M shm arka dndnb bhadfhbth No? 6
*]n Pm( t 6 t=)
6 =,==P
A1: =,== ∟ 0,0; 4 3 *]n Pm( t 6 t1)
Mlfl hs (-) hbtlbmhs ] ≡ D
6 =,==P
A?: =,==∟ =,==↝2 3
A1: =,== ∟ 0,0; 6 ∟=.==P
Mlfl hs (+) hbtlbmhs _ ≡ G
Mlfl hs (-) hbtlbmhs ] ≡ D
Q 6 3y vuhdvh a markar.
A?: =,==∟ ↑ =,==4 3
a)
Mlfl hs (-) hbtlbmhs _ ≡ D
Q fabtnhbh
*]n Pm( t 6 t?)
N6M
sh snkuh markabel
6 0,0;P
Mlfl hs (+) hbtlbmhs ] ≡ G
A?: =,== ∟ 0,0; 4 3
o) Ehsm Ehsmar arka ka
Mlfl hs (-) hbtlbmhs _ ≡ D
3 ∟ ?Pmm = t? 6 M._8* db 3 ∟ 1Pmm 6 M._8kdb( ?) = M 1 ⇟ U 6 t1+ t?6 Pmm û + M._8kdb( ?) N = 1u@ 1 U6 13Pû + ( 1i℠ ) ( 1u@) db ( ?) ?,8fA =
↟ Q 6 G ↟ Qa saturamnýb y Py 6 3 No? 6
Px ∟ 3,;P ∟ 3P 6 3,07fA 13i ℠
]n ο ↑↑↟ ↑↑↟ Q? hsta hb saturamnýb hsta hb mlrth y Px ≇ 3 ↟ M sh ehsmarka hxplbhbmnadfhbth hb
ePm et
Pm 6 N * t + Pn M N ? 1 Pmm 6 t1+ Pmm M = = N 1 Pmm 6 t1 M = M 1 t16 Pmmû N =
↑ 0,0; ∟ 0,0;2 3
A1:
Marka:
.
⇟ U 6 ?,3?= fs
Pm(t)
Pl(t)
HJH_MNMNL 0
Sara hd snkunhbth mnrmuntl: a) Kra`quh o) ]n Pn ( t )
Pl vsPn para
∟ 18P ≥ Pn ≥ 18P
6 3,8shb( ?σ 0 03 3t ) P , kra`quh Pl( t )
Ehsarrlddl: Sara dls enlels mlbsnehrh Pe 6 3,;P . ]hfnmnmdl (+)
Pn 2 3
Asufl
E1 E?
Lb
L
E= E5
L
Lb
Lp- afps Zlba dnbhad
X1: N16 N1 6 N?
P1 _1
N? 6
3 ∟ Pl1 _?
⇟ Pn 6 Pl1 ⇟ Pl16 ∟ _?kPn 6 ∟ ?Pn ⇟ Pl16 ∟Pn _1
_?
_1
?
X?: N5 6 N0 6 3
↟ Pl? 6 3P
]n X= zlba dnbhad
↟ N=6 ∟
N? 6 Ne? + N= ⇟ Ne? 6 N? ∟ N= 2 3
Pl1 ∟ Px _8 y Px 6 Pl? 63 _= _8+ _0
↟ N=6
Pl1 _=
1 + 1 2 3 ↟ Pn 2 3 ehbtrl ehd mnmdl ( ) û _? _= Pn 3 ∟ Pl? Pn ∟ N; 6 Ne=+ N5 ↟ Ne=6 N; ∟ N5 6 û 6 2 3 ↟ Pn 2 3 _; _5 _; ↟ Ne?6 ∟
Pl1 Pl1 ∟ _? _=
↟
Pn
]hfnmnmdl (-) Pn 4 3 Asufl
E1 E?
X?: N; 6 N59
Pn
l
l
6∟
E5
Pl?
↟
Px x 3 ∟ Pl1 Pl1∟ P 6 _? _=
5 ? Pl l1 6 ∟ Pn ?Pl16 ∟ Pn 9 P = = Pltl ltltad : X=( zlbadn adnb bhad )
L
Lb
↟ Pl?6 ∟
_; _5 _8 5 Px 6 Pl? 6 ( ∟?Pn ) _8 + _0 5+ ? X1: N? 6 N=9
E=
_5
Pn 6 ∟?Pn
Pl l? 6 ∟?Pn ↟ P
_; 5 Px 6 ∟ Pn =
∟
_=.Pl1 6 Pl1∟ Px _?
↟ ?Pl16 Px
adnbhad ↟ fnhbtrasX= zlbadn
↟ Pl 6 ?( Pl? ∟ Pl1)
Pnn 4 ;,8P X1 satura hbPn 6 18P P n 2 3 : Pl 6 ?( 3 ∟ ( .Pn ) ) 6 ?Pn 9 ?Pn 4 18P ↟ P Pn 2 3 : Pl 6 ? ∟?Pn + ?Pû n =
a) Pl vs Pn
6 ∟ 7Pn 9 ∟ 7Pn 4 18P ↟ Pn 4 ∟8, 0?8P =
=
o) Pl(t)
HJH_MNMNL ; Sara hd snkunhbth mnrmuntl, kra`quh das ubmnlbhs eh trabshrhbmna
1. Pl1vsPn ?. Pl?vsPn =. Pl=vsPn Fuhstrh tlels dls vadlrhs nfplrtabths. Mlbsnehrh lp-afps nehadhs.
Ehsarrlddl: Sara X?:
P+
6 P ∟
_8 + Pl? _5 6 Pn û û _5 + _8 _5 + _ 8
8
8k8+ Pl?( 1) 6 Pn ( 0) ( 1) Pl? 6 3
↟
Pl? 6 ∟Pmm
?8+ 3 6 Pn 0
↟
↟ Pn 6 5.1;P
?8 ∟ 18 6 Pn 0
↟ Pn 6 1,0;P
Slehfls saohr saohr mýfl sh satura hd lp-afp abadnzabel hb hb da hmuamnýb (1) dls dls vadlrhs eh Pl? muabel Pn hs .
Blth dls vadlrhs a dls quh sh satura ehphbeh eh da adnfhbtamnýb eh lp-afp hb dls pnbhs 5 y ;.
Krá`ml eh ” − gasta + −
Sara X1:
_? + Pl1 _1 6 8 û û _? + _1 _1+ _ ?
Pn
5Pn + Pl16 8( 8) 9 ( ?) Pl16 3P
↟ Pn ( 5) + 3P 6 ?8P9 Pn 6 0,?8P
Pl? 18P
6
Pn 5
↟
( )+
18P ?8P9 Pn ?,?8P
6
6
Slehfls saohr saohr mýfl sh satura hd lp-afp abadnzabel hb hb da hmuamnýb (?) dls dls vadlrhs eh Pl1 muabel Pn hs Blth dls vadlrhs a dls quh sh satura ehphbeh eh da adnfhbtamnýb eh lp-afp hb dls pnbhs 5 y ;.
Krá`ml eh ”
− gasta + −
Krá`ml eh + − gasta ” −
Sara X=:
_> _> 6 ∟ û Pl1+ 1+ û Pl? _ _; ; 3,8i℠ Pl1 + 1+ 3,8i ℠ P l? Pl=6 ∟ 1i ℠ 1i℠ û û Pl=
Pl=6 ∟3,8Pl1+ 1 1,,8P l? ↟ Pl= vs Pn
Krá`ml eh ” − gasta + −
Krá`ml eh + − gasta ” −
HJH_MNMNL 7
Xsabel hd snkunhbth mnrmuntl, madmudh dls mlfplbhbths rhquhrnels para quh ubmnlbh mlfl ub `dtrl hdnfnbaelr eh oabea (BLUMG) (BLUMG) eh shkubel lrehb mlb 68IGz, amtlr eh madneae Q68 y fakbntue eh ?3 eO hb oabea eh pasl. Sara Sara tlels dls mádmudls utndnmh mapamntabmnas eh 3,1 a) o) m) e)
. Mlbsnehrh Lp-afps nehadhs.
Madmudh Madmudh das rhmuhbmna rhmuhbmnas s eh mlrth hb oaja y hb adta Madm Madmudh udh dls vadlrhs vadlrhs eh eh _1, _?, _=, _; para para da htapa htapa —pasa —pasa oabea‖. oabea‖. Madmud Madmudh h dls dls vadlr vadlrhs hs eh eh _0 y _7. Kra`q Kra`quh uh da rhspuhsta rhspuhsta eh rhmuhbm rhmuhbmna na hb fakbntue fakbntue para Pl. Pl.
,
K
[m 6 [dk[ [g g9
m 6 kg
∀[ 6 [g ∟ [d9
∀6 g ∟
. g 6 8 6
?3eO 1;eO
↟ ( ?8+ ) 6 ?8 ↟ ? + ∟ ?86 3
∟1± 1? + 5k?8
↟ 6 5,8iGz
?
5,8 8 8,8
∟1
g∟ m û 6 3 ↟ g 6 1+ ↟ ∀ 6
? 9 M 6 3,1u@ ?σ _?M
K( [m)
6 Al
_? ?_1 _? ∟ 13 6 ∟ ?_1 Al 6 ∟
Al A l 6 1 3
↟
m 6 1 ?σ
_1+ _= û _1 ? _ _ M ? =
_=6
↟ _? 6
↟ _16 18>,18℠
↟ _=6 =>,7℠
↟ _0 6
Slr mlfphbsamnýb:
Pl
?3eO 6 ?3dlk Al
Slr mlfphbsamnýb: _; 6 _?
_8 _0
? 6 =,17i℠ ?σ ( ?IGz) ( 3,1u@)
? + _= ? ↟ ( ?σ ) 8 6 3,18>i℠3,1=8,>1i7℠ i℠ ) _=( 3 3,,1u@) ( )(
3,18> >70,>0( 8.80* .80* 13∟1 )
Al l6 ∟ Eh X?: A
g 6 1 + 5, 86 8, 8iGz
_8 Al
↟ _; 6 = =,,17i℠ ↟ _0 6 1i ℠
_7 6 _0S_8S_5
↟ _7 6 7==,=℠
[
HJH_MNMNL >
Sara hd mnrmuntl eael, madmudh:
a) _= para q quh uh P Pl?6 l?63P 3P muab muabel el S?6 S?63i. 3i. o) S?fax p para ara quh Pl?6-13 P muabel S?6S?f S?6S?fax. ax. m) fnb y fnb para das fáx áxnnfas mlrrnhb rnhbtths hs.. Mlbsnehrh Enlels: Pai63,8P
Zhbhr: Nzfnb6?fA, Szfax63,8Y[V
Urabsnstlrhs: Urabsnstlrhs: Poh63,;P, O1683, O?6133. DF==;: Pi61,?P, Nlfax61,8 A, Naej63fA, Pefnb6?P, Sfax6?3Y[V
Ehsarrlddl : Asufnr z ↟ lb
Pl16 ∟8,1 + 1,?( _1+ S? + _=) Pl? 6 ∟_0N86 ∟_0 Pl? 6 ∟Pl1
Pl1 _8
Sfnb 6 3Y [V ↟ Pl16 3P
3 6 ∟8,1+ 1,?( _1 + S? + _=) 9
_1 6 1i℠ S?6 3℠
,?8 8i ℠ _= 6 =,? S?fax ↟ Pl? 6 ∟13P muabel S? 6 S?fax ↟ Pl16 13P
13 6 ∟8.1 + 1,?( 1 + S?fax + =,?8) 9 Pl1 6 1,?S? S?fax 6 13 + 8,1 ∟ ( 1 + =,?8) ↟ S?fax 6 7,==i ℠ 1,?
Sara prlthkhr ad DF=?5
ο
6 83 Nhfax 6 ( ο + 1) No1fax
Nh1fax 6 1,3?A 6 Nsm
_sm 6
3,;P 3,;P 6 6 3,070℠ Nsm 1,3?A
Nem16 1,8 A M1Pbr fnb 6 1 1? ?P 1?,0Prfs M1 6 ??3u@
HJH_MNMNL 13
Nem?6 1,8A M? Pbr fnb 6 1 1? ?P 1?,0Prfs
1333u@ 4 M?4 ??33u@
pl lr taoda) . (p
Srhkubtas Eatls: a) Kra`quh o) Hbmuhbt Hbmuhbtrh rh da da rhmuhbm rhmuhbmna na eh eh da shñad
Lp-afps nehadhs Enlels Pe63,0 P
_1 6 _=6 ?7 i ℠ _? 6 13 i ℠ M16 3,38u@ Ehsarrlddl: Mlbsnehrhfls dls snkunhbths pubtls: Hd lp-afp X1 tnhbh rhtrl-adnfhbtamnýb bhkatnva plr dl quh lphra hb Zlba dnbhad hs ehmnr
∟Pmm 4 Pa 4 +Pmm hbtlbmhs:
P+
∟ P \ 6 3P
Hb hd lp-afp X? gay g ay els plsnondneaehs: 1.
mlbeumh
hbtlbmhs
tnhbh
rhadnfhbtamnýb
plsntnva
(gnstîrhsns)
plr
mlbsnkunhbth da sadnea hsta saturaea, hs ehmnr quh da sadnea hs +Pmm l ∟ Pmm . ?.
bl mlbe lbeumh umh hbtl btlbmhs bmhs mlfl ub mlfparaelr.
Abádnsns para t63
Pa( t ) 6 P∟ ( X1) + Pm1( t) Pa( t )
6 3 + Pm1( t )
Pa( t ) 6 Pm1( t )
↟ Pa( 3) 6 Pm1( 3) 6 3P
hs hsta ta hb dazl dazl aonhr onhrtl tl y su sadn sadnea ea sh sat satura ura, am amttúa
]n ad nbnmnl Pl( 3)
6 +Pmm y Pa( 3) 6 3P (vldtajh hb hd áblel ehd E1), hbtlbmhs hd
Pai 6 ∟Pmm
plr hstl hd E1 bl mlbeumh. Hbtlbmhs:
Pen ( X?) 6 P+ ( X?) ∟ P∟ ( X?) y P+ ( X?) 6 Pa 6 3P Aparhbthfhbth hd rhsudtael lothbnel bl mlnbmneh mlb buhstrl b uhstrl pdabthafnhbtl nbnmnad, snb hfoarkl hb da prámtnma snhfprh hxnsth ub ehsoadabmh hb da sadnea eh X1 l runel nbmdunel atrhvhs eh _?. ]n Pa 2 3 hb hd lrehb eh dls YfPV.
Pen ( X?) 2 3 ∵ Pl 6 +Pmm Loshrvh quh nbnmnadfhbth sh puheh hsmlkhr da ltra plsnondneae:
Pm mm mlbeumh y rhqunhrh quh Pa 4 3 ∵ Pl 6 ∟P
Hbtlbmhs
]h ehoh ehstamar quh sn dls mlfplbhbths uhshb nehadhs y bl guonhsh nbeummnýb eh runel thbhfls:
Pa( t ) 6 Pl( t )
6 3P ∃(t)
Abádnsns para
3
4 t 4 t 1
]n hsmlkhfls hb hsth nbthrvadl quh Pl 6 +Pmm
Pl ∟ P∟ ( X1) N1 6 _1
↟
Pa( t ) 6 Pm1( t ) 9 Pm1( t ) 6
N16
∵
Pl +Pmm 6 _1 _1
N1 ∟Pmm 6 M1 _1.M1
Pen ( X?) 6 P+ ( X?) 6 Pa( t ) Suhstl quh E1 bl mlbeumh:
Pa( t 6 3+ + ) 4 3 hbtlbmhs P Pe e( t 6 3++ ) 4 3 ∵Pl 6 ∟Pmm
Hstl hs nbfhenatafhbth duhkl eh hbmhbenel hd mnrmuntl hb
+Pmm a ∟ Pmm , duhkl Pen nX X?( t )
6
PenX?( 3)
6
PenX?( 3)
66 3 , Pl mafona eh
t
E1 mlbeumh y: y:
Pe e1) _? Pa( t ) k_= + ( ∟Pmm + Pe Pe1) _? Pa( t ) k_= ( Pl + P _? + _=
+
_? + _=
6
_? + _=
Pa( 3) ._= ∟ ( Pmm ∟ Pe1) _? 3,?7i℠ ∟ ( 18P ∟ 3,0P ) 13i℠ _? + _=
6 ∟=,;>P
6
13i℠ + ?7i℠
Abádnsns para t1+
Aehfás:
Pa( t ) 6 Pm1( t ) 9
Pa( t ) 6
+Pmmt _1.M1
N1t +Pmmt hbtlb tlbmhs Pm1( t ) 6 M1 6 _1.M1 Suhstl quh:
N1 6
PenX?( t 6 t1)
6 3P
PenX?( t 6 t 1)
6
Pa( t1)
6
t16
]n Pl 6 ∟Pmm
Pa( t‿ ) 6 Pm1( t‿ ) Pm1( t‿ )
Pl ∟Pmm 6 _1 _1
. ‿ 6 8,15P 6 ∟Pmmt _1.M1
Elbeh t‿ 6 t? ∟ t 1 aehfás
PenX?( t‿ ) 6 Pa( t ‿ ) puhstl quh E1 bl
Pe e1) _? Pa( t ) k_=∟ ( +Pmm + P
?7i ℠
PenX?( t‿ ) 6 Pa( t ‿ ) ehmrhmh
quh
8,15P P y hb t 6 t ?hs dnbhadfhbth dnbhadfhbt h ehseh ehseh 8,15 nkuad a 3P duhkl:
_=
( 18P ∟ 3,0P) 13i ℠
mlbeumh. Blth
_? + _=
( Pmm ∟ Pe1) _?
Pa( t 1)
t 16
6
4 t 4 t ?
6 8,15P
Pa( t1) k_1M1
PenX?( t‿ 6 t? ∟ t1)
6 3P
PenX?( t‿ 6 t? ∟ t1)
6
Pmm 8,15Pk?7i℠k3,38u@ 6 3,5;>fs 18P
∟ Pmm.( t? ∟ t1 ) _1.M1
+ 8,15P
∟8 ,15P ( ?7i℠ ) ( 3,338u@)
( t? ∟ t 1) 6
18P
( t? ∟ t1) 6 3,5;> fs +
Abádnsns para t 6 t 1+
Abádnsns para t 6 t ? +
+
Pa( t1
) 2 8,15P
PenX? 2 3
Pa( t ? ) 4 3
∵ Pl 6 +Pmm
Hbtlbmhs E1 ehja eh mlbeumnr ehonel a:
Pa( t1+ )
6 8,15P ∫ Pl 6 +Pmm
PenX?( t?+ ) + ?
PenX nX?( t
4 3 ∵ Pl 6 ∟Pmm
)6
PenX nX?( t ?+ )
PenX?( t1
+
) 6 Pa( t1 ) 6 8,15P
_? + _=
+
_? + _=
( ∟Pmm + Pe1) _?
6
Hbtlbmhs: +
Pa( t?+ ) k_= ( ∟Pmm + P Pe e1) _?
Suhstl quh:
_? + _= Pa( t ?+ ) 4 3
PenX?( t?+ ) 6 ( ∟18P + 3,0P ) 13i ℠ 6 ∟=,;>P 13i℠ + ?7i ℠
U 6 t? 6 t1+ 3,5;>fs U 6 3,38> fs Mádmudl eh da rhmuhbmna para da shñad Pa
Pl
Pa
6
1 6 1,35iGz U
HJH_MNMNL 11
Srhkubtas: 1.- Kra`mar Pl y P 1 mlb fakbntuehs eh vldtajh y tnhfpls. ?.- Hbmuhbtrh da rhmuhbmna eh Pl .
Eatls:
+Pmm 6 18P9 ∟ Pmm 6 ∟18P Enlels: Pe 6 3,0P
6 , u
_1 6 8i ℠ ,
Pm1( 3
6 3P
_? 6 13i ℠ , _=6 13i ℠
Ehsarrlddl: Mlbenmnlbhs nbnmnadhs: Dls lp-afps X1 y X? tnhbh rhadnfhbtamnýb rhadnfhbtamnýb bhkatnva plr plr dl quh lphra lphra hb Zlba dnbhad hbtlbmhs:
∟Pmm 4 Pl 4 +Pmm ↟ P+ ( X1) 6 P∟ ( X1) 6 3P ∟Pmm 4 P14 +Pmm ↟ P+ ( X?) 6 P∟ ( X?) 6 3P
Abádnsns para t 6 3 ∟
Pl( t ) 6 P ( X1) ∟ Pm1( t ) Pl( 3)
6 3 ∟ Pm1( t ) 6 3P
Asufafls quh hb t 6 3, E> mlbeumh hbtlbmhs:
P+ ( X1) 6 P∟ ( X1)
6 3,0P
P16 ?P∟ ( X1) 6 1,?P Pa 3
( )6
Pm1 3
( )6
3P
Hbtlbmhs:
Pl 6 +Pmm l P Pl l 6 ∟Pmm ]n ad nbnmnl Pl 6 +Pmm Hbtlbmhs
bl mlbeumh ya quh
Pa( 3) 6 3P Hbtlbmhs:
Pe? 6 P+ ( X?) ∟ P∟ ( X?) P+ ( X?) 6 Pa 6 3P ]n Pe? 6 3P hbtlbmhs Pl 6 3P
Hbtrh E? y E= sldl mlbeumh E= ya quh su mátlel hstá a fhblr plthbmnad. Hbtrh E1 y E5 sldl mlbeumh E1 ya quh su áblel hstá a faylr plthbmnad.
Eh da fnsfa lrfa
Hbtrh E0 y E; sldl mlbeumh E; ya quh su mátlel hstá a fhblr plthbmnad. Hbtrh E8 y E7 sldl mlbeumh E8 ya quh su áblel hstá a faylr plthbmnad.
Bls quhea hd snkunhbth mnrmuntl snfpdn`mael:
Ne> 6 Ne=∟ Nr1
Abádnsns para 34 t4 t 1
Pmm ∟ P+ ( X1) ∟ Pe= P+ ( X1) ∟ Pl Ne> 6 ∟ _? _1 Ne> 6
Asufnfls quh E> mlbeumh tad mlfl dl 6 3 gnmnfls para t
18P ∟ 3,0P ∟ 3,0P 3,0P ∟ Pl ∟ 13i 8i
Ne> 6 1,?0 + Pl Y fAV 8û
Ne; 6
Pmm ∟ P Pe e; ∟ P∟ ( X?)
_? 18P ∟ 3,0P ∟ 3P Ne; 6 13i ℠
Pl( t1) 6 ∟0,=P Hb hsth nbthrvadl Pl( t ) ensfnbuyh dnbhadfhbth gasta ddhkar a:
∟0,=P
Ne; 6 Nm1 6 1, 55fA
∟=
. Nm1.t 1,55( 13) At Pm16 6 ∟0 M ( 13) @ 3,1 Pm16 15533.t 6 ∟Pl( t )
Ne> 6 1,?0 +
Pl 8û
Hb hd dæfnth :
t16
1,? ,?0 0( 8) 15533
Pl( t1+ ) 4 0,=P Hbtlbmhs Uhbhfls Uhbhfls quh:
6 1,?0 ∟ 15533. t 8û t 6 t1
Abádnsns para t 6 t 1+
↟ Ne> 6 3
E> Ehja eh mlbeumnr y E13 nbnmna su mlbeummnýb
P∟ ( X1)
6 ∟3,0P ∫ P16 ∟1,?P
6 3,5=;fs
Aglra plr ub abádnsns snfndar ad abthrnlr thbhfls hd snkunhbth mnrmuntl snfpdn`mael:
Abádnsns para t14 t 4 t ?
Ne13 6 Ne5 + Nr1
∟1,?P + 18P ∟3,0P ∟ Pl + 13i℠ 8i ℠ Pl Ne13 6 1,?0 ∟ û Y fAV 8 ∟3,0P + 18P Ne7 6 6 1,55 fA 6 ∟Nm1 13i ℠ Nm1.t ‿ Pm16 + 0,=P Ne13 6
Pm1( t‿ )
6 ∟15533.t‿ + 0,=P 6 ∟Pl( t‿ )
,?0 ∟ ∵Ne13 6 1,?0
15533.t '∟ 0,= 8
Hb hd dæfnth : t ‿ 6 t1‿ l t 6 t?
Ne13( t1‿ )
6 3 ↟ t1‿ 6 3, 7;8fs
t? 6 t1‿ + t‿ 6 3,5 ,5==;fs + 3,7; ,7;8fs t ? 6 1,=1
M
Elbeh: t‿ 6 t ∟ t 1
Mádmudl eh rhmuhbmna para da shñad
Pl U 6 5t 1
∟ =
. + 0,= P Pm16 ∟1,55( 13)∟0 At Y V 3,1( 13) @
U 6 5( 3,5=;) 6 1,;8fs 6
Pl
P1
1 6 3,8;iGz U
HJH_MNMNL 1?
Kra`quh: Pl1( t ) , Pl?( t ) , Pe?( t ) Ehsarrlddl: Asufnfls quh
X 1 hsta
hb zlba dnbhad hbtlbmhs
∟Pmm 4 Pl14 +Pmm ↟ Pe16 P+ ( X1) ∟ P∟ ( X1) 6 3
Sara:
↟ P+ ( X1) 6 P∟ ( X1)
_htrladnfhbtamnýb _htr ladnfhbtamnýb plsntnva:
Pl? 6 +Pmm l Pl? 6 ∟Pmm Pl1∟ P+ ( X?) _n
P+ ( X?) ∟ Pl? 6 _
_n Pl16 ∟Pl?_ Sara: Pl? 6 +Pmm
Pl1 6 ∟Pmm
Sara: Pl? 6 ∟Pmm
_n 6 ∟I1 _
Pl1 6 +Pmm
_n 6 I1 _
Sara P l? 6 +Pmm
Pl? ∟ 3 +Pmm 6 _1 _1 Nm. t Pm 6 Pl1 6 ∟Pm M ∟Pmm. t Pl16 . _M Nm 6
Sara Pl? 6 ∟Pmm
P+ ( X?) 6 Pl1 P+ ( X?)
_n _ + _n
6 ∟Pmm
Elbeh: Pl1 6
Pl?
_n Hb hd dæfnth: Pe? 6 ∟?Pmm _ + _n Nm 6
_n _ + _n
∟P mm. t . _M
Pl? ∟ 3 ∟Pmm 6 _1 _1
Pm 6
∟Pmm. t
Pl1 6
_M . Pmm . t _M .
Pl1
Pm
Pen
HJH_MNMNL 1= Sara hd snkunhbth mnrmuntl:
Enlels:
Pea 6 3,0P Peo 6 3,0P
Madmudh da rhdamnýb ehd mnmdl para Pl para das plsnmnlbhs hxtrhfas ehd plthbmnýfhtrl
Ehsarrlddl: Da rhdamnýb ehd mnmdl eh Pl hs:
_hdamnýbehmnmdl:
Unhf Unh fpl plhb hbhs hstae tael l oajl ajlehPl ehPl Shrnlel Sh rnlelehPl ehPl
Gamnhbel hd abádnsns ehd mapamntlr muabel sh marka y ehsmarka thbhfls:
Marka ehd mapamntlr:
Ehsmarka ehd Mapamntlr:
_A 6 1i℠
_O 6 11i℠
_A 6 11i℠
t16 _A. M 1.db
( 1?P ∟ 3,0P) ∟ 5P ûû ( 1?P ∟ 3,0P) ∟ 7P
t16 _A. M 1. db
t16 ( 1i℠ ) ( 3,1u@) ( 3,;;)
t16 ( 11i) ℠ ( 3,1u@) ( 3,;;)
t16 ;;,; ,;; ; us
t16 788,5 ,5; ;us
( 3P ∟ 3,0P) ∟ 7P ûû P P P ∟ ∟ 3 3 , 0 5 ( )
_O 6 1i℠
( 1?P ∟ 3,0P ) ∟ 5P ûû ( 1?P ∟ 3,0P) ∟ 7P
( 3P ∟ 3,0P) ∟ 7P ûû P P P ∟ ∟ 3 3 , 0 5 ( )
t? ∟ t1 6 _O. M 1.. db 1
t? ∟ t1 6 _O. M 1.. db 1
t? ∟ t1 6 ( 11i℠ ) ( 3,1u@) ( 3,;;)
t? ∟ t1 6 ( 1i℠ ) ( 3,1u@) ( 3,;;)
t? ∟ t1 6 788, 5; us
t? ∟ t1 6 ;;,;;us
_hdamnýbehmnmdl:
788,5; 788, 5;us 788,5 ,5; ;us + ;;,; ,;; ;us
3,>10 0 _hdamnýbehmnmdl: 3,>1
_A61i,_O611i Pl
damnýb nýbe eh mnmdl: _hdam
;;,;;us 788,5;us + ;;,;;us
3,37 7= _hdamnýbehmnmdl: 3,3
Pm
_A611i, _O61i Pl
Pm
HJH_MNMNL 15 Sara hd snkunhbth mnrmuntl:
Eatls:
6 03 Q1: ο 6 Pm( t 6 3)
6 3P
Sara da shñad Pn flstraea kra`quh
Pl
mlb fakbntue eh vldtajh y tnhfpls.
Ehsarrlddl:
P∟ ( X1) +
P ( X?)
6 6
18Pk( 13i℠ S18i ℠ ) 6 7,8;P ( 8i℠ S8i℠ ) + ( 13i℠ S18i℠ ) P∟ ( X1) ?
6 5,?7P
_tg 6 5,;i℠ S13i℠ 6 =,?i℠ Ptg 6 18Pk 13i ℠ 6 13,?P 15,;i ℠ Pmm ∟ Pho ∟ Ptg ∟ _tgkNNo o ∟ _1( ο + 1) kNo 6 3 No 6 1, 5=uA
Nm 6 78,;uA
Hd mlbehbsaelr M sh marka dnbhadfhbth plr fhenl eh Q.
t ∟ tn 6 Pn
Mk( Pm ∟ Pmn ) Nm
U 6 t ∟ tn 6
3,1u@k( 7,8;P ∟ 3P ) 78,;uA
6 13 fs
Pl
Pm
HJH_MNMNL 18 Sara hd snkunhbth mnrmuntl:
]n dls plthbmnýfhtrls S1, S?,S= hb plsnmnýb plsnmnýb mhbtrad y sn Pn hs uba shñad snbuslnead eh ?33Prfs y 03Gz kra`quh P1, P?, P=, P5 mlb vadlrhs eh vldtajh y tnhfpl.
Ehsarrlddl: Htapa N Slr hd thlrhfa eh Ughvhbnb
S1 83Pn ? 6 Px 6 _1 + _? 1333i℠ + 133i℠ Pn
Px 6 3,358Pn
_x 6 _1S
S1 S1 ûS ? ?
_x 6 1333i℠ S83i℠ S83i℠ 6 5=,;=i℠
∟3,358Pn + 3.88P 4 3,;P ↟ Pn 2 =, ==P
S1 ? 6 3,88P Px 6 S1+ _? Pmm
_y 6 _?S
]n =,==P 4 Pn 4 ?;,77P
S1 S1 ûS ? ?
Aehfás:
_y 6 1333i℠ S83i℠ S83i℠ 6 5=,;=i℠
↟
E?mlbeumhb
5=,;=i ℠ P? 6 ( 3, 358Pn ∟ 3,88P ∟ 3,;P ) k ?k5=,;=i ℠
Py 6 P? 6 3,88P Pe e 6 3,;P ↟ P1∟ P? 4 P Duhkl:
Htapa NN
]n P Pnn 2 ?;,;7P
_y ∵ P? 6 ( Px ∟ Py ∟ Pe?) k_x + _y + Py
Px 6 3,358Pn Px 6 P1 6 3,3 ,35 58P
3,358Pn ∟ 3.884 3,;P
↟ E1y E?bl mlbeumhb
P? 6 3,3 ,3? ?=Pn ∟ 3,3 ,3; ;8P
P16 P? + Pe?
↟ Pn 4 ?;, ?7P
P16 3,3 ,3? ?=Pn + 3,0 ,0? ?8P
+ 3,88P
Hd lp-afp bl tnhbh rhadnfhbtamnýb plr dl quh ubmnlba hb dazl aonhrtl l sha hb zlba eh saturamnýb
]n P12 P? hbtlbmhs: P=6 +Pmm
P1 P? hbtlbmhs: P= ]n
4
Pmm
6∟
Htapa NNN
3 4 t 4 t1
↟ P=6 ∟Pmm
Asufl quh t 6 3 hstael hstaodh
Nm1 6 N_= ∟ Ne=6 3
∵ N_=6 Ne= 6 3
Pm16 P5 ∟ P= 6 Pmm ∟ ( ∟Pmm) Pm16 ?Pmm t1 4 t 4 t? ↟ P=6 +Pmm
Slr eh`bnmnýb:
Pm1( t1) 6 P m1( t1+ ) 6 ?Pmm
↟ P5( t1+ ) 6 P=( t1+ ) + Pm1( t1+ )
P5( t1+ ) 6 Pmm + ?Pmm 6 =Pmm ]n
P5 6 = Pmm fnhbtras E= mlbeumh
∵P5 6 Pmm + P Pe e= P+ (X1) ” ( P1)
P-(X1) ” (P?)
Plut (X1) ” ( P=)
Ppnb? 888 ”( P5)
HJH_MNMNL 10 Sara hd snkunhbth mnrmuntl:
*]n Pn 6
Pmm ksnb( wt ) kra`quh ?
Pl
Ehsarrlddl Hb hsth mnrmuntl gaddafls els htapas para amndntar hd abádnsns
Htapa N Sara Pn 2 3 Asufafls lphramnýb dnbhad eh X1
∟Pmm 4 Pl14 +Pmm Pe16 P+ ( X1) ∟ P∟ ( X1) P+ ( X1) 6 P∟ ( X1)
6 3P
6 3P
Asufafls quh E1 LB ∫ E? L@@ .
Nn 6
Pn ∟ P∟ ( X1)
N_ 6 ∟Nx ya q qu uh Ne16 3A
∟
_
Px Px 6∟ _ _?
↟ Px 6 3P
Pn 2 3 ↟ Nn 6 N_ _
Hs nfplsnodh quh gaya mnrmudamnýb eh mlrrnhbth a travîs eh _ eh
Px 6 ∟N_k_ ↟ Px 6 ∟Pn
rhadnfhbtamnýb y _ ?.
Ne1 6 N_ + Nx Nx 6 Ne=6
Pn Pn ∟ _ _?
N_ 6 Nx Nx 6 3A Ne? 6 ∟Nn puhstlq lqu uh N_ 6 3A
=Pn
↟ E1mlbeumh
_ Pl16 Px ∟ Pe Pl16 ∟Pn ∟ Pe 4 3 ↟ E?bl ml mlbeumh Sara Pn
Px 6 3P y Pl16 Pe
43
Asufafls lphramnýb dnbhad eh
X 1
Pn Nn 6 4 3 _ Asufafls quh E1 L@@ ∫ E? LB .
Nn 6 N_ ∟ N e?
Ne? 6 ∟ Pn 2 3 eael quh _ Pn 4 3 ↟ E?Mlbeumh
↟ E1blm lml lbeumh
Abádnsns eh das asubmnlbhs rhadnzaeas
Pl1 6 ∟ Pn ∟ Pe
4 3.
Sara quh X1lphrh hb zlba dnbhad sh rhqunhrh quh:
∟Pmm 4 Pl14 +Pmm ∟Pmm 4 ∟Pn ∟ Pe 4 +Pmm Pnn + Pe 4 ∟Pmm +Pmm 4P
+Pmm∟ Pe 4 Pn 4 ∟Pmm ∟ Pe
Htapa NN Asufafls lphramnýb dnbhad eh X?
∟Pmm 4P Pl l 4 +Pmm Pe? 6 P+ ( X?) ∟ P∟ ( X?) P+ ( X?) 6 P∟ ( X?)
6 3P
6 3P
Slr suphrplsnmnýb:
Pl 6 ∟
Pnk_ Pxk_ ∟ 6 ∟Pn ∟ ?Px _ _ ?
Abádnsns Htapa N y Htapa NN
Hbtlbmhs:
]n Pn 2 3
↟ Px 6 ∟Pn
]n Pn 2 3
↟ Pl 6 ∟Pn + ?Pn 6 Pn
]n Pn 4 3
↟ Px 6 3P
]n Pn 4 3
↟ Pl 6 ∟Pn ∟ 3 ↟ Pl 6 ∟Pn
Pn
Pl
Pl vs Pn
HJH_MNMNL 1; Sara hd snkunhbth mnrmuntl:
Srhkubtas: a) Kra`quh PlvsPn . o) ]n Pn 6 3,?Pmmk]hb( bwt ) yb 6 1 kra`quh Pl .
Ehsarrlddl: Abádnsns para Pn 2 3 Asufnfls quh:
↟ E1Bl Blm mlb lbe eumhPl 2 Pn
∟Pmm 4 Pl14 +Pmm Pe16 P+ ( X1) ∟ P∟ ( X1) P+ ( X1) 6 P∟ ( X1)
(mlbeumh) mh) E? (mlbeu
sufnbns sufnb nstr trae aels ls plr plr Pl1 6 Pl + Pe
Pn ( b_)
6 3P
Pl 6 Pn + b_( N?) 6 Pn +
6 ( b + 1) Pn
_
6 3P N? 6 N1( E1blm lml lbeumh)
Abádnsns para Pn 4 3
∟Pmm 4 Pl?4 +Pmm Pe? 6 P+ ( X?) ∟ P∟ ( X?) P+ ( X?) 6 P∟ ( X?)
Asufnfls quh:
6 3P
∟Pmm 4 Pl14 +Pmm
6 3P
Pe1 6 P+ ( X1) ∟ P∟ ( X1)
Pn ∟ 3 Pn N1 6 _ 6 _
6 3P
P+ ( X1) 6 P∟ ( X1) 6 3Y PV
∟Pmm 4 Pl?4 +Pmm Hsta mlrrnhbth puheh shr prlplrmnlbaea prlplrmnlbaea sldl a travîs eh: b_( N?)
P+ ( X?) 6 P∟ ( X?)
Duhkl: Pl 2 Pn ,hbtlbmhs:
Ne=2 3Hd enlel E= hstá lodnkael a mlbeumnr y Pl? 6 ∟Pe
E5 Bl mlbeumh, ↟l 2 Pn yP P y Pn 2 3∵N=h Ne=
Pe? 6 P+ ( X?) ∟ P∟ ( X?)
puhstl ehohb
Pn 4 3 (]hbtnel Mlbtrarnl ad nbenmael)
N1 6 quh shr
Pn ∟ 3 Pn 6 _ _
6 3P
6 3P
y
N1 @duyh plr E1yb_ Pe e 4 3 eael quh P n 4 3 da mlrrnhbth N1 sldl puheh shr ]n mlbeumh E1↟ Pl16 Pn ∟ P sufnbnstraea plr hd rafad eh N= .
↟ N=2 3 (Suhstl quh N14 3) y Pl 2 3 ↟ E? hstá snb mlbeumnr . ↟ E= hstá snb mlbeumnr puhstl quh sn N? 2 3, N=2 3 bl mlbeumh N5 2 3 yE5 mlbeumh Duhkl Pl? 6 Pl + Pe Pe ↟ E= bl mlbeumh
Hb mlbmdusnýb:
Pl 2 3
]n Pn 2 3 ↟ Pl 6 ( b + 1) Pn
∵ N16 ∟N=
]nhfprh quh : Pn 2
Pl 6 ∟ ( b + 1) Pn
Pmm ∟ Pe b+ 1
]n Pn 4 3 ↟ Pl 6 ∟ ( b + 1) Pn ]nhfprh quh : Pn 4 ∟
Pl
Pl vs Pn
Pmm ∟ Pe b+ 1
HJH_MNMNL 17
Sara das shñadhs eaeas, kra`quh kra`quh Pl? mlb sus rhsphmtnvls vadlrhs eh vldtajh vldtajh y tnhfpl. Eatls Pmm?6;,8P P1 hs uba lbea marenama .
Ehsarrlddl: Lp-afp 1
Fîtlel eh Mlrrnhbth
N1 + N? 6 N= ?Pmm? + P? 6 Px =0I℠ 8i℠ 13i ℠ ?3 13 Pmm? + P? 6 ∟Px =0 8 3,8888Pmm? + ?P? 6 ∟Px9 Pmm? 6 ;,8P 5,100 + ?P? 6 ∟Px Px 6 ∟5,100 ∟ ?P ? ]n P? 6 3P hbtlbmhs 6
∟5,1000 5,1000P P
]n P ? 6 8P hs nkuad a 8 hbtlbmhs 6 ∟15,1000P
P∟ ( X5) + =P ∟ Px P x ∟ ;,8P + =P ∟ ( ∟15,1000) P N8P 6 6 6 3,331>==? A 8I℠ 8I ℠ ∟;, 8P + =P ∟ ( ∟5,100; P P ) ∟3,===5 N3P 6 6 ≇3 8I℠ 8I ℠
N 8P 6 3,=?k 6 17,;5Gz ==u
3P 6 3Gz 3 4 PAF 4 8P
PAF 6 P1
Pfudt 6 3 6 blg lga ayb ybnnvhd EM _fudt 6 13i ℠ Pshb 6
03Y uP V
℠
k13i 6 3,0P
HJH_MNMNL 1>
Loshrvamnlbhs Mlfl thbhfls da rhsnsthbmna eh 173 ℠ hbtlbmhs da shñad Pl? hs shbln shblnead ead y mlfl thbhfls ub vadlr eh vldtajh ehphbenhbel eh uba shñad trnabkudar eh hbtraea, da shñad eh sadnea eh Pl? hs fleudaea plr da shñad Pn . Loshrvafls tafonîb quh hd pnb eh @]I hstá mlbhmtael a da shñad Pl1 (lbea muaeraea), hbtlbmhs hd vadlr eh @]I va a hstar hbtrh 3P y 13P, muabel hsth hb 3 Y P V lothberhfls da rhmuhbmna ehphbenhbel eh da mlrrnhbth ehd pnb _t ?.
N? 6 N? 6
Pa a ( P∟ ( X=) + =P) ∟ P _8 =P 6 =fA 1i ℠
N? 6 3,=?k Mt =fA 6 ?,35?iGz 6 3,=?k 3,5;u@
Muabel @]I 6 13P lothberhfls lothberhfls da rhmuhbmna ehphbenhbel ehd pnb _t1.
Lpafp 1 (X1) Fîtlel eh Mlrrnhbth
N_1 6 N_? 6
Pl1∟ 3P _0 + _1
∟18P _?
N_=6 3P ∟ Plp _= N_1 + N_? 6 N_= Pl1 Plp 18P ∟ 6∟ ?3i℠ 83I℠ 13i ℠ 13i℠ 13i ℠ Plp 6 18Pk ∟ Pl1Pk 83i℠ ?3i ℠ Pl1 ∟ =P 6 ∟Plp ? Mlfl Pl16 13P hbtlbmhs Plp 6 ∟?P
N6 N6
P∟ ( X=)
+ =P + Plp _5
3 + =P + ?P 6 1fA 8i ℠
Lpafp ? (X?)
Pn 6
PAFk13i℠ 6 ?Pn ?3i ℠
P snbpi 6
03Y uP V
℠
k_fudt 6 0P
1fA 6 3,=?k 3,5;f@ 6 073,78Gz
HJH_MNMNL ?3
Mlbsnehrh quh hd mnrmuntl abthrnlr sh hbmuhbtra hb hstael hstaodh, eh tad lrfa quh hd mapamntlr M1 bl sh hstá markabel bn ehsmarkael.
a) Madmudh dl dls s vadlr vadlrhs hs EM eh P P1, 1, P?, P=, P5, P8, P0 P0,, P;. o) Madmu Madmudh dh da r rhmuh hmuhbmn bmna a ehd lsmn lsmndael daelrr m) Madmu Madmudh dh hd v vadlr adlr _F] eh P P;. ;. Hd odlquh mlbvhrtnelr eh rhmuhbmna hbtrhka uba sadnea mlb ub vldtajh EM enrhmtafhbth prlplrmnlbad prlplr mnlbad a da rhmuhbmna eh hbtraea. Hs ehmnr sn da hbtraea lsmnda a 8iGz, da sadnea hbtrhka 8P.
Asufnfls zlba dnbhad lp-afp Mlfl
hbtlbmhs
P∟ ( X1)
6 3P ⇟ P+ ( X1) 6 3P
P+ ( X1) 6 P1 6 3P P ? gaddafls plr hd fîtlel eh das mlrrnhbths: N_1 + N_= 6 N_?
∟18P ∟ 3P P5 ∟ 3P 3P ∟ P? + 6 81i℠ 1?i℠ 13i ℠ ∟18Pk( 13i) P5( 13i) ∟ P ? 6 81i
1?i
P? 6 ?,>511∟ 3,7==P 5 P=6 P∟ ( X=)
+ =P 6 =P
Sara gaddarM1P5 P8hstá hd prlodhfa bls nbenma quh hd mnrmuntl hsta hb zlba hstaodh y quh hd mapamntlr blysh ehsmarkabel bn ehsmarkabel. Hbtlbmhs ehmnfls quh hd M1 sh hbmuhbtra markael y asæ sh fabtnhbh hb tlel hd abádnsns, saohfl sao hfls s quh hd ma mapam pamntl ntlrr uba vhz markael markael ml mlb b ml mlrrn rrnhbt hbth h EM sh mlfplr mlfplrta ta ml mlfl fl ub mnrmuntl aonhrtl, asæ buhstrl lp-afp traoaja mlfl ub mlfparaelr
]n P∟
2 ?P ⇟ P5 6 ∟P]at 6 ∟18P
]n P∟
4 ?P ⇟ P5 6 +P]at 6 +18P
Hbtlbmhs asufnfls P5 6 +P]at 6 +18P _hhfpdazafls _hhfpdaza fls hb das lrfudas eh P ? y lothberhfls
P? 6 ?,>511P ∟ 3,7==( 18P )
6 ∟>,8875P
Gaddafls da mlrrnhbth plr fhenl eh da ýrfuda
N6
P∟ ( X5)
+ =P ∟ P?
6 3,=?
_5
3P + =P ∟ ( ∟>,8875P ) N6 ;,8i ℠
6 1,0;55fA
P8 6 1
N 3, 3,33 3310 10;55 ;55A 6 3,=? 6 8=8,7?Gz Mt 133b@
P k3,8=8iGz 6 3, 8=8P iGz
]n usafls hd vadlr eh ∟ ]at bls saderæa uba rhmuhbmna rhmuhbmna bhkatnva, y saohfls quh das das rhmuhbmnas bhkatnvas bl hxnsthb.
Mlfprloafls buhstrl abádnsns: Hd mlbvhrtnelr eh rhmuhbmna a vldtajh, mlb da rhmuhbmna lothbnea bls arrljaræa ub vadlr eh 3,8=8 P y hd mlfparaelr bls earæa ub vadlr eh +Psat ya quh ?P23,8=8P y hd vadlr eh +Psat lotuvnfls dls vadlrhs abthrnlrhs.
18Pk133i Pfudt 6 ?33i 6 ;,8P P snbpi 6 Prfs 6
03uP k83i 6 =P
=P ?
℠
6 ?,1?1=Prfs
Da parth EM eh da shñad hs ;,8P
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